Nanson's method
Encyclopedia
The Borda count
can be combined with an Instant Runoff procedure to create hybrid election methods that are called Nanson method and Baldwin method.
.
Nanson's method eliminates those choices from a Borda count tally that are at or below the average Borda count score, then the ballots are retallied as if the remaining candidates were exclusively on the ballot. This process is repeated if necessary until a single winner remains.
and works like this:
Candidates are voted for on ranked ballots as in the Borda count. Then, the points are tallied in a series of rounds. In each round, the candidate with the fewest points is eliminated, and the points are re-tallied as if that candidate were not on the ballot.
: since Borda always gives any existing Condorcet winner more than the average Borda points, the Condorcet winner will never be eliminated. They do not satisfy the independence of irrelevant alternatives
criterion, the monotonicity criterion
, the participation criterion
, the consistency criterion
and the independence of clones criterion
, while they do satisfy the majority criterion
, the mutual majority criterion
, the Condorcet loser criterion
, and the Smith criterion
. The Nanson method satisfies reversal symmetry
, while the Baldwin method violates reversal symmetry
.
town of Marquette, Michigan
in the 1920s. It was formally used by the Anglican Diocese of Melbourne
and in the election of members of the University Council of the University of Adelaide
. It was used by the University of Melbourne
until 1983.
Borda count
The Borda count is a single-winner election method in which voters rank candidates in order of preference. The Borda count determines the winner of an election by giving each candidate a certain number of points corresponding to the position in which he or she is ranked by each voter. Once all...
can be combined with an Instant Runoff procedure to create hybrid election methods that are called Nanson method and Baldwin method.
Nanson method
The Nanson method is based on the original work of the mathematician Edward J. NansonEdward J. Nanson
Edward John Nanson was a mathematician known for devising Nanson's method , a variation of the Borda count using successive elimination down to the winner....
.
Nanson's method eliminates those choices from a Borda count tally that are at or below the average Borda count score, then the ballots are retallied as if the remaining candidates were exclusively on the ballot. This process is repeated if necessary until a single winner remains.
Baldwin method
This variant was devised by Joseph M. BaldwinJoseph M. Baldwin
Joseph Mason Baldwin was Victorian government astronomer 1920–1943.Baldwin was born in Carlton, Melbourne, Australia, the third son of Joseph Baldwin and his wife Emma Maria, née Graham. J.M...
and works like this:
Candidates are voted for on ranked ballots as in the Borda count. Then, the points are tallied in a series of rounds. In each round, the candidate with the fewest points is eliminated, and the points are re-tallied as if that candidate were not on the ballot.
Satisfied and failed criteria
The Nanson method and the Baldwin method satisfy the Condorcet criterionCondorcet criterion
The Condorcet candidate or Condorcet winner of an election is the candidate who, when compared with every other candidate, is preferred by more voters. Informally, the Condorcet winner is the person who would win a two-candidate election against each of the other candidates...
: since Borda always gives any existing Condorcet winner more than the average Borda points, the Condorcet winner will never be eliminated. They do not satisfy the independence of irrelevant alternatives
Independence of irrelevant alternatives
Independence of irrelevant alternatives is an axiom of decision theory and various social sciences.The word is used in different meanings in different contexts....
criterion, the monotonicity criterion
Monotonicity criterion
The monotonicity criterion is a voting system criterion used to analyze both single and multiple winner voting systems. A voting system is monotonic if it satisfies one of the definitions of the monotonicity criterion, given below.Douglas R...
, the participation criterion
Participation criterion
The participation criterion is a voting system criterion. It is also known as the "no show paradox". It has been defined as follows:* In a deterministic framework, the participation criterion says that the addition of a ballot, where candidate A is strictly preferred to candidate B, to an existing...
, the consistency criterion
Consistency criterion
A voting system is consistent if, when the electorate is divided arbitrarily into two parts and separate elections in each part result in the same choice being selected, an election of the entire electorate also selects that alternative...
and the independence of clones criterion
Independence of clones criterion
In voting systems theory, the independence of clones criterion measures an election method's robustness to strategic nomination. Nicolaus Tideman first formulated the criterion, which states that the addition of a candidate identical to one already present in an election will not cause the winner...
, while they do satisfy the majority criterion
Majority criterion
The majority criterion is a single-winner voting system criterion, used to compare such systems. The criterion states that "if one candidate is preferred by a majority of voters, then that candidate must win"....
, the mutual majority criterion
Mutual majority criterion
The mutual majority criterion is a criterion used to compare voting systems. It is also known as the majority criterion for solid coalitions and the generalized majority criterion...
, the Condorcet loser criterion
Condorcet loser criterion
In single-winner voting system theory, the Condorcet loser criterion is a measure for differentiating voting systems. It implies the majority loser criterion....
, and the Smith criterion
Smith set
In voting systems, the Smith set, named after John H. Smith, is the smallest non-empty set of candidates in a particular election such that each member beats every other candidate outside the set in a pairwise election. The Smith set provides one standard of optimal choice for an election outcome...
. The Nanson method satisfies reversal symmetry
Reversal symmetry
Reversal symmetry is a voting system criterion which requires that if candidate A is the unique winner, and each voter's individual preferences are inverted, then A must not be elected. Methods that satisfy reversal symmetry include Borda count, the Kemeny-Young method, and the Schulze method...
, while the Baldwin method violates reversal symmetry
Reversal symmetry
Reversal symmetry is a voting system criterion which requires that if candidate A is the unique winner, and each voter's individual preferences are inverted, then A must not be elected. Methods that satisfy reversal symmetry include Borda count, the Kemeny-Young method, and the Schulze method...
.
Use of Nanson and Baldwin
Nanson's method was used in city elections in the U.S.United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
town of Marquette, Michigan
Marquette, Michigan
Marquette is a city in the U.S. state of Michigan and the county seat of Marquette County. The population was 21,355 at the 2010 census, making it the most populated city of the Upper Peninsula. Marquette is a major port on Lake Superior, primarily for shipping iron ore and is the home of Northern...
in the 1920s. It was formally used by the Anglican Diocese of Melbourne
Melbourne
Melbourne is the capital and most populous city in the state of Victoria, and the second most populous city in Australia. The Melbourne City Centre is the hub of the greater metropolitan area and the Census statistical division—of which "Melbourne" is the common name. As of June 2009, the greater...
and in the election of members of the University Council of the University of Adelaide
University of Adelaide
The University of Adelaide is a public university located in Adelaide, South Australia. Established in 1874, it is the third oldest university in Australia...
. It was used by the University of Melbourne
University of Melbourne
The University of Melbourne is a public university located in Melbourne, Victoria. Founded in 1853, it is the second oldest university in Australia and the oldest in Victoria...
until 1983.
Note
Advocacy
- A case for Baldwin's Method by Ian Fellows